There are plenty of bars, cafes, discotheques and restaurants in the area around of the Plaza de Armas, in the centre of Cusco. It is not without reason that nights out in Cusco are some of the best you will have in South America. Many of the establishments mentioned are open early for tourists.
You can choose between:

A quiet walk through the typical and traditional neighbourhoods of Cusco combined with a visit to some of the modern parks that have not lost their traditional touch. For example the neighbourhood of San Blas or Hatunrumiyoc.

A quiet dinner, in a typical or modern restaurant, enjoying an infinity of international and national dishes, including the typical dishes of the region.

You can also enjoy a cup of coffee and famous national and international liquors in karaoke bars, pubs, cafes, and other similar establishments.

And of course there are a vast number of discotheques for young people and people who like to dance and make new friends from a variety of nationalities!